How do you make bullets do damagein the BGE?
Your problem might be that the character is not detecting the collision from a static object. If you make your bullet a rigid body object, with all of the translations locked (rotation and location along X,Y, and Z) as in this picture,



Your bullet will have the same behavior as a static object (It will not fall due to gravity and it will not bounce off of other objects), but the rigid body type can detect collisions with a static object. Another thing you could try is changing the collision bounds on both your character and the bullet to something closer to it's actual shape. Normally, a box will work for the projectile, but for the character you will want something more precise such as a Triangle Mesh